If the measures of the interior angles at vertex A- B- and C are 5x-60-2x-40- and 3x-80- - respectively- then find the measure of x in the given triangle-

Given: The measures of the interior angles at vertex A, B, and C are nbsp; (5x 60^∘),(2x+40^∘), and (3x 80^∘), respectively. As per the angle sum property, th ...

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Standard VII

Mathematics

Introduction to Triangles

If the measur...

Question

If the measures of the interior angles at vertex $A, B,$ and $C$ are $(5 x - 60^{\circ}), (2 x + 40^{\circ})$ , and $(3 x - 80^{\circ})$ , respectively, then find the measure of $x$ in the given triangle.

28^{\circ}

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26^{\circ}

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32^{\circ}

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30^{\circ}

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Solution

The correct option is A $28^{\circ}$
Given: The measures of the interior angles at vertex $A, B,$ and $C$ are
$(5 x - 60^{\circ}), (2 x + 40^{\circ}),$ and $(3 x - 80^{\circ})$ , respectively.
As per the angle sum property, the sum of the three interior angles of a triangle is $180^{\circ}$ .
So,

$(5 x - 60^{\circ}) + (2 x + 40^{\circ}) + (3 x - 80^{\circ}) = 180^{\circ}$ $\Rightarrow 5 x - 60^{\circ} + 2 x + 40^{\circ} + 3 x - 80^{\circ} = 180^{\circ}$ (Opening the brackets)
$(5 x + 2 x + 3 x) + (- 60^{\circ} + 40^{\circ} - 80^{\circ}) = 180^{\circ}$ (Grouping the like terms together)
$\Rightarrow 10 x - 100^{\circ} = 180^{\circ}$
$\Rightarrow 10 x - 100^{\circ} + 100^{\circ} = 180^{\circ} + 100^{\circ}$ (Adding $100^{\circ}$ on both sides of the equation)
$\Rightarrow 10 x = 280^{\circ}$
$\Rightarrow x = 28^{\circ}$

$\to$ Option B is correct.

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If the measures of the interior angles at vertex A,B, and C are (5x−60∘),(2x+40∘), and (3x−80∘) , respectively, then find the measure of x in the given triangle.

If the measures of the interior angles at vertex $A, B,$ and $C$ are $(5 x - 60^{\circ}), (2 x + 40^{\circ})$ , and $(3 x - 80^{\circ})$ , respectively, then find the measure of $x$ in the given triangle.